We study the large deviations of time-integrated observables of Markov diffusions that have perfectly reflecting boundaries. We discuss how the standard spectral approach to dynamical large deviations must be modified to account for such boundaries by imposing zero-current conditions, leading to Neumann or Robin boundary conditions, and how these conditions affect the driven process, which describes how large deviations arise in the long-time limit. The results are illustrated with the drifted Brownian motion and the Ornstein–Uhlenbeck process reflected at the origin. Other types of boundaries and applications are discussed.

中文翻译：

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反射扩散的动态大偏差

我们研究了具有完美反映边界的Markov扩散的时间积分可观测量的大偏差。我们讨论了如何通过施加零电流条件（导致Neumann或Robin边界条件）来修改用于动态大偏差的标准频谱方法以解决此类边界问题，以及这些条件如何影响驱动过程，从而描述了在驱动过程中出现大偏差的情况。长期限制。漂移的布朗运动和原点反映的Ornstein-Uhlenbeck过程说明了结果。讨论了其他类型的边界和应用程序。